Solve (a^2)^3+(b^2)^3

$$( a ^ { 2 } ) ^ { 3 } + ( b ^ { 2 } ) ^ { 3 }$$

Evaluate

$$a^{6}+b^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$a^{6}+\left(b^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$a^{6}+b^{6}$$

Factor

$$\left(a^{2}+b^{2}\right)\left(a^{4}-a^{2}b^{2}+b^{4}\right)$$

Solution Steps

Rewrite a^{6}+b^{6} as \left(a^{2}\right)^{3}+\left(b^{2}\right)^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

$$\left(a^{2}+b^{2}\right)\left(a^{4}-a^{2}b^{2}+b^{4}\right)$$